Clifford’s Geometric Algebra offers a new perspective on vector spaces, accommodating elements of any dimension. Vectors, bivectors, scalars, rotors, and multivectors play key roles in this algebra. The Geometric Algebras for 2D and 3D vectors naturally incorporate rotations, with the 2D algebra resembling complex numbers and the 3D algebra mirroring quaternions. Projective Geometric Algebra expands into an extra dimension to handle points, lines, and planes, while Conformal Geometric Algebra adds two extra dimensions to represent various geometric elements like circles and spheres. Rotation, translation, and dilation operations are unified in these algebras, offering a unique approach to geometric transformations.
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